What has advanced

The selected no-common-phase route has an explicit hypothesis audit. The local source admits an ordinary differential symbol, but its composed response symbols have not been identified.

The information lost under smooth residual testing is also explicit: attachment-diagonal covectors may disappear from every tested kernel. Pointwise-in-$G$ regularity does not replace a joint microlocal theorem.

Finally, two valid preliminary factor products do not make their final product valid. The retained characteristic cancellation persists in the ordinary operator/pullback test without invoking a common phase or an excess bundle.

These results exclude an automatic factorwise shortcut. They do not exclude every possible no-common-phase construction of the complete coefficient.